Question

The manager of a hardware store knows that the weekly revenue function for batteries sold can be modeled with R(x) = -x^2 + 10x + 20000, where both the revenue R(x) and the cost x of a package of batteries are in dollars. What amount of sales would give the maximum revenue? What is the maximum revenue?

Answer 1

Answer: The amount of sales that would give the maximum revenue is 5Rs , and the maximum revenue would be 20,025Rs.

Explanation:

To find the amount of sales that would give the maximum revenue, we need to determine the value of x that maximizes the revenue function R(x) = -x^2 + 10x + 20000.

The revenue function is a quadratic equation, and the maximum value occurs at the vertex of the parabola.

In this case, the equation is R(x) = -x^2 + 10x + 20000, so a = -1 and b = 10. Substituting these values into the formula, we have:

x = -10 / (2 * -1)

x = -10 / -2

x = 5

Therefore, the amount of sales that would give the maximum revenue is Rs5.

R(5) = -(5)^2 + 10(5) + 20000

R(5) = -25 + 50 + 20000

R(5) = 20025